An individual entire wealth is from one stock. The current value of the stock is $55 and the individual owns one million shares. This individual purchased puts on the stock with an exercise price of $52 to protect his wealth. He bought enough puts to protect his entire holdings of this stock. The expiration of the put is 4 years. Immediately after buying the puts he was appointed to a 4-year government position and was told that if want to stay in the government position his return over the next two years must exactly equal the risk-free rate. The risk-free rate is 10%. 

You have been asked to construct a spread that will provide the investor with a return over the next two years that exactly equals the return from the risk-free return on his stock holdings. You can only buy the minimum number of needed derivatives given the investors current holdings. A speculator is willing to sell or buy from you any option with any strike price with a two- year exercise.

Questions:

Part 1. Describe in detail the derivatives you would utilize to achieve the desired payoff.

Part 2. Draw the payoff graph for the spread.

Part 3. Show the detailed payoffs from each derivative at all relevant stock price ranges.